Ocean temperature and salinity surface observations can be extrapolated to depths in the ocean by known methods, and the errors in performing such an extrapolation can be reduced, also according to known methods. However, vertical gradients tend to remain overly smooth. What is currently done is that the average temperature and salinity over various horizontal distances at each depth of interest are determined for normal conditions in a particular location.
Operational ocean forecasting systems rely on a relative abundance of ocean surface observations for data assimilation into numerical models. Commercial fishermen utilize ocean forecasts to identify productive fishing grounds associated with ocean fronts and other dynamic ocean features. All numerical ocean forecasts rely on data assimilation. A common component of these systems aggregates surface observations and projects surface information downward to estimate the 3-dimensional temperature and salinity structure of the global ocean. Traditionally, systems minimize analysis temperature and salinity differences from observations using a least squares minimization technique. The cost function J in equation (1), an exemplary cost function of Fujii and Kamachi, A reconstruction of observed profiles in the sea east of Japan using vertical coupled temperature-salinity EOF modes, J. Oceanography, 59, 2003, 173-186, includes terms that minimize the temperature and salinity differences of the analysis from the first guess and observations.
                                                        J              =                                                                                            1                  2                                ⁢                                                      (                                          x                      -                                              x                        fg                                                              )                                    T                                ⁢                                                      B                                          -                      1                                                        ⁡                                      (                                          x                      -                                              x                        fg                                                              )                                                              +                                            I                                                                                                                                                          1                  2                                ⁢                                                      (                                                                  H                        ⁢                                                                                                  ⁢                        x                                            -                                              x                        0                                                              )                                    T                                ⁢                                                      R                                          -                      1                                                        ⁡                                      (                                                                  H                        ⁢                                                                                                  ⁢                        x                                            -                                              x                        0                                                              )                                                              +                                                          I              ⁢                                                          ⁢              I                                                                                                                                                    1                                  2                  ⁢                                      r                    h                    2                                                              ⁢                                                (                                                            h                      ⁡                                              (                        x                        )                                                              -                                          h                      0                                                        )                                2                                                                        I              ⁢                                                          ⁢              I              ⁢                                                          ⁢              I                                                          (        1        )            where x represents a vector of the analysis solution temperature and salinity values being sought. The xfg is the first guess ocean state vector, and x0 is the observations vector. The error covariances, B and R, are constructed using well known data assimilation methods. The matrix H transforms the analysis to the observation space. Term III minimizes differences of the analysis, h(x), and observed, h0, sea surface height anomaly, where rh2 is the standard deviation of the sea surface height anomaly. The cost function in equation (1) provides no constraint on the vertical gradients of temperature and salinity, and the entire ocean depth is handled in one minimization.
While the system minimizes the temperature and salinity errors, vertical gradients tend to remain overly smooth and unrealistic (see FIG. 1 PRIOR ART). Variation in vertical gradients can change the acoustic transmission loss prediction as shown. Accurate representation of the vertical gradient is also important for prediction of ocean currents. What are needed are improved synthetic ocean profiles of temperature and salinity that avoid an overly smoothed ocean vertical structure. What is further needed is to more accurately predict the vertical structure of the ocean through the use of the improved synthetic ocean profiles in numerical ocean models.